Remark 7.10 Spielman's [1]} proof of Corollary REF  in the case of unit edge weights and Chung's [2]} proof of Corollary REF  used Theorem REF  applied to the combinatorial and normalised Laplacians, respectively. Coutinho, Grandsire and Passos in [3]} gave a proof of Corollary REF  in the case of unit edge weights using interlacing.
